Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 221 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.If 8 notebooks cost ₹144, how much do 11 notebooks cost? (a) ₹147 (b) ₹198 (c) ₹1584 (d) ₹216
2. 2.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 1 day
3. 3.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹6 (b) ₹12 (c) ₹24 (d) ₹18
4. 4.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 12 days (d) 4 days
5. 5.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹170 (d) ₹238
6. 6.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹333 (b) ₹37 (c) ₹370 (d) ₹185
7. 7.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹42 (b) ₹294 (c) ₹142 (d) ₹63
8. 8.If 2 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹96 (b) ₹48 (c) ₹33 (d) ₹64
9. 9.If 5 mangoes cost ₹115, how much do 4 mangoes cost? (a) ₹115 (b) ₹460 (c) ₹114 (d) ₹92
10. 10.If 3 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹70 (b) ₹56 (c) ₹168 (d) ₹43
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
13. 13.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 3 days (d) 28 days
14. 14.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 13 days (d) 11 days
15. 15.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹160 (b) ₹80 (c) ₹20 (d) ₹140
16. 16.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 11 days (d) 45 days
17. 17.If 7 pens cost ₹63, how much do 8 pens cost? (a) ₹64 (b) ₹504 (c) ₹81 (d) ₹72
18. 18.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
19. 19.If 9 mangoes cost ₹162, how much do 5 mangoes cost? (a) ₹158 (b) ₹810 (c) ₹108 (d) ₹90
20. 20.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹32 (d) ₹8
21. 21.If 3 pens cost ₹15, how much do 2 pens cost? (a) ₹30 (b) ₹10 (c) ₹14 (d) ₹15
22. 22.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 14 days (d) 15 days
23. 23.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹25 (b) ₹16 (c) ₹20 (d) ₹60
24. 24.₹168 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹140 (b) ₹168 (c) ₹84 (d) ₹28
25. 25.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹135 (d) ₹15
26. 26.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 24 days (d) 6 days
27. 27.If 8 mangoes cost ₹24, how much do 9 mangoes cost? (a) ₹30 (b) ₹27 (c) ₹25 (d) ₹216
28. 28.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹283 (d) ₹282
29. 29.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹198 (d) ₹220
30. 30.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 7 days (d) 10 days
31. 31.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹176 (b) ₹192 (c) ₹160 (d) ₹32
32. 32.If 8 kites cost ₹120, how much do 6 kites cost? (a) ₹105 (b) ₹90 (c) ₹720 (d) ₹118
33. 33.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 2 days (d) 14 days
34. 34.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹31 (b) ₹50 (c) ₹120 (d) ₹40
35. 35.If 4 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹49 (b) ₹168 (c) ₹30 (d) ₹42
36. 36.If 9 pens cost ₹99, how much do 7 pens cost? (a) ₹88 (b) ₹693 (c) ₹77 (d) ₹97
37. 37.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹40 (c) ₹32 (d) ₹8
38. 38.If 8 kites cost ₹168, how much do 12 kites cost? (a) ₹252 (b) ₹172 (c) ₹2016 (d) ₹273
39. 39.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹378 (c) ₹294 (d) ₹210
40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days

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